Theo Walcott, left, and Danny Welbeck were just two of England's young players who made an impact against Sweden in Kiev. Photograph: Lee Smith/Action Images

Fabio Capello used to wonder aloud why even England's most experienced players were undermined by fear. As the noise subsided after Friday night's 3-2 victory over Sweden, it looked very much as though the Italian's comparatively homely successor has found a way of banishing that nameless dread.

After a tentative draw against France, secured by the diligence of a resilient rearguard, Roy Hodgson was able to enjoy signs of individual initiative in a tense and ultimately tumultuous victory in Kiev. He had made it possible, first by backing Andy Carroll to succeed against a defence noted for succumbing to aerial attack, and then by taking a chance on the pace and directness of Theo Walcott to reverse the flow of a game that appeared to be slipping out of England's grasp.

Only four matches and a handful of training sessions into the job, the manager deserves credit not just for those tactical decisions – one of them the product of careful consideration and the other made on the hoof – but for enabling England to demonstrate they can, after all, transfer the sort of spirit they show for their clubs into their performance in the national shirt. Even at this early stage, his equally unpretentious assistants, Ray Lewington and Gary Neville, should share some of the praise.

Remember this was only Sweden, a team beaten four days earlier by Ukraine, who in turn were comfortably seen off by France on Friday evening. England had never beaten the Swedes in a competitive match before, making the victory worth a double celebration, although Hodgson had never lost to them in four matches with Switzerland and Finland. But for all Zlatan Ibrahimovic's brooding menace, this is not the side of Henrik Larsson, Martin Dahlin and Tomas Brolin, never mind of Nils Leidholm, Gunnar Nordahl and Gunnar Gren. They came to the Euro 2012 finals with a head coach, Erik Hamren, who is trying to get them to break away from their long-established pattern of play – and on the evidence presented so far, he cannot be said to be succeeding.

When you score two goals against England in a tournament match of some significance, however, you might expect to be celebrating. Seldom can a player have accepted a man of the match award with a more woebegone expression than Olof Mellberg, who had earlier exulted in the opportunist shot – diverted first by Joe Hart and then by Glen Johnson – and the excellent header that capped Sweden's domination of the match's third quarter. Unwisely, perhaps, Uefa's presenter asked, in English, what it meant to him. "Not a lot," the former Aston Villa defender replied.

In two days' time, England will face Ukraine, for whom reaching the quarter-finals would represent satisfaction in a tournament on home soil. Probably 90% of the 50,000 seats in the Shakhtar Donetsk stadium will be occupied by home fans desperate for Andriy Shevchenko to lead their team beyond the group stage. At least now England will take to the pitch knowing they possess a strength of will that enabled them to rise above what might have been a terminal slump in morale created by Mellberg's efforts, even if they still have a lot of work to do on their ability to pass the ball safely out of deep midfield, a weakness that will take more than a couple of weeks to eradicate and which is likely to catch them out against any of the tournament's better teams.

But leave such reservations for another day and enjoy the rollercoaster ride of Friday's win, so exact in its reproduction of the way a good Premier League match can tug the emotions this way and that before lurching to a shuddering, agonising climax.

England's players at least have plenty of experience of that sort of scenario. Once Walcott's stunning arrival had restored their self-belief, they showed that they knew how to cope, which was not by simply sitting back and absorbing punishment. In the third minute of injury time, Walcott tore down the right wing again and delivered an accurate ball for Steven Gerrard, who might have widened the margin had Andreas Isaksson not produced the last of several excellent saves.

The first of them had come in the seventh minute, when Danny Welbeck set up Scott Parker for a drive that arced off the outside of the Tottenham player's right boot and was heading for the top corner. But little more than a quarter of an hour later the former Manchester City goalkeeper, now with PSV Eindhoven, would have needed Ronnie Hellstrom and Thomas Ravelli, two former Swedish goalkeeping heroes, alongside him to have had a chance of impeding the progress of Carroll's magnificent header as it flashed into the bottom left-hand corner. The opening had been made by a diagonal ball from Steven Gerrard that, although not from a dead-ball kick, strongly resembled the one with which the captain inspired Joleon Lescott's goal against France. Bisecting Mellberg and Andreas Granqvist like a lance between the shoulder blades, it allowed Carroll to demonstrate the enduring value of old virtues.

England's other goals were the product of moves more in keeping with the ideals of modern football. Walcott, a 61st minute substitute for the labouring James Milner, had been on the field for three minutes without touching the ball when he met the clearance from a corner with a first-time shot that flew over the morass of yellow-and-blue shirts and under the middle of the crossbar from 25 yards out. In the 78th minute, shortly after Kim Kallstrom had failed to make the most of a good opportunity to restore Sweden's lead, Walcott scooted down the right flank in familiar fashion and pulled the ball back for Welbeck, whose improvised finish – not quite a pirouette, as Hodgson later described it, but balletic nevertheless – delighted the eye and settled Sweden's hash.

The return of Wayne Rooney on Tuesday will necessarily mean the removal of one of the players who made a substantive contribution to Friday's victory. Given that Rooney and Welbeck are team-mates at Old Trafford and enjoy the basis of an understanding, it will probably be Carroll who is invited to step down.

Hodgson appreciates James Milner's doggedness, so the Manchester City man may keep his starting place, but it was particularly pleasing to see Walcott not just scoring again for England, more than four years after his celebrated hat-trick in Zagreb, but demonstrating an ability to come off the substitutes' bench and influence the course of an evening.

Those of us who, since the retreat from Baden-Baden in 2006, have been screaming for England to put their faith in a younger generation will have derived almost as much pleasure as Hodgson from the sight of players in their early 20s – Carroll, Walcott, Welbeck – prepared to impose themselves on the contest in the Olympic Stadium, particularly in that terrific last half-hour, when anxiety might have taken hold.

Anything England achieve in this tournament, under a manager shoehorned into the job at such short notice, is a bit of a bonus, but after this they will be looking forward to the next instalment with justified optimism and no fear.